CN115630577A - Downscaling rainfall prediction method and system - Google Patents
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Abstract
The invention provides a method and a system for predicting downscaling rainfall, which belong to the technical field of rainfall prediction, wherein rainfall grades are divided for each station, the station grades and the station intervals are combined and considered in resolving a geographical weighted regression model of the station, after a regression coefficient and a residual error result of each station are obtained by resolving, interpolation is carried out in a grid under high resolution to obtain a regression coefficient and a residual error result of each grid under high resolution, rainfall data are further obtained, and prediction of the rainfall data under high resolution is realized; moreover, the grade and the distance between the stations are simultaneously considered in the weight function, so that compared with the method of directly interpolating according to the rainfall data of the stations, the rainfall data prediction accuracy of the sparse area of the stations is guaranteed, and the comparison shows that the rainfall data predicted from the target area is richer in details by adopting the method of simultaneously considering the distance between the stations and the grade between the stations.
Description
Technical Field
The invention relates to the technical field of rainfall prediction, in particular to a downscale rainfall prediction method and system.
Background
Rainfall is one of the important factors of climate change, has important effects on atmospheric processes on different spatial scales, and accurate prediction of rainfall has important significance in the fields of agriculture, disaster prevention and reduction and the like, and particularly high-resolution rainfall data becomes the key for solving relevant work in the fields of agriculture and disasters.
The traditional method for acquiring high-resolution rainfall data is obtained by performing direct interpolation based on site data, but the method is limited by the influences of the distribution density, the quality and the like of the acquired site data, and the direct interpolation method has certain limitations in remote areas with sparse sites such as mountainous areas. Therefore, how to accurately predict rainfall data at high resolution becomes a key to solving related work in the fields of agriculture and disasters.
Disclosure of Invention
The invention aims to provide a downscaling rainfall prediction method and system, which can accurately predict high-resolution rainfall data.
In order to achieve the above object, in one aspect, the present invention provides a method for predicting downscaling rainfall, including:
and grading each site according to the historical rainfall data of each site in the target area, and determining the rainfall grade of each site.
Based on a cross validation method, determining the window width of the geographical weighted regression algorithm according to the rainfall observation value of each station in the target area.
And determining a weight function between any two stations based on the rainfall level of each station, the window width and the space distance between every two stations.
Aiming at any station, establishing a geographical weighted regression model of the station by taking the rainfall observed value of the station as a dependent variable and taking a plurality of auxiliary variables of the station as independent variables; the geographic weighting regression model comprises parameters to be determined; the parameters to be determined comprise regression coefficient matrixes and residual error results of the auxiliary variables; the auxiliary variables include parameters characterizing the geographical location of the site, the topography of the site, or the extent of vegetation coverage of the site.
Aiming at the geographical weighted regression model of any station, solving to obtain a regression coefficient matrix and a residual error result in the geographical weighted regression model of the station according to the station and a weight function between the station and each station except the station in the window width range; the window width range is an area centered on the station and having the window width as a radius.
And carrying out interpolation in the target area according to the regression coefficient matrix and the residual error result in the geographical weighted regression model of each site to obtain the regression coefficient matrix and the residual error result of each grid under high resolution.
And predicting the rainfall of each grid according to the regression coefficient matrix and the residual error result of each grid under high resolution to obtain a rainfall prediction value of each grid.
Optionally, the predicting rainfall of each grid according to the regression coefficient matrix and the residual result of each grid under the high resolution to obtain a rainfall prediction value of each grid specifically includes:
and aiming at any grid under the high resolution of the target area, determining a rainfall non-residual estimation value of the grid according to a regression coefficient matrix of the grid and an auxiliary variable value of the grid.
And obtaining the rainfall estimation value of the grid according to the rainfall non-residual estimation value of the grid and the residual result of the grid.
Optionally, the determining a weight function between any two stations based on the rainfall level of each station, the window width, and the spatial distance between each two stations specifically includes:
and determining the grade weight between any two sites according to the rainfall level of each site.
And determining the distance weight between any two stations according to the space distance between every two stations and the window width.
And determining a weight function between any two sites according to the grade weight between any two sites and the distance weight between any two sites.
Optionally, the distance weight between any two sites is determined according to:
wherein,
is the distance weight between site i and site j, d ij Is the spatial distance between site i and site j, and b is the window width.
Determining a rank weight between any two sites according to:
wherein,
is a rank weight between site i and site j, C ij Is the rank difference between site i and site j, C max Is the maximum value of the grade difference.
Determining a weight function between any two sites according to:
wherein, W ij As a function of the weights between site i and site j,
as a rank weight between site i and site j,
the distance between site i and site j is weighted.
Optionally, the stations are classified by adopting a natural fracture method according to historical rainfall data of the stations in the target area, and the rainfall grade of each station is determined.
Optionally, interpolation is performed in the target area by using a common kriging method to obtain a regression coefficient matrix and a residual error result of each grid under high resolution.
Optionally, the window width of the geoweighted regression algorithm is determined according to:
wherein, b best The window width of the geographic weighted regression algorithm determined based on the cross validation method is defined, n is the number of sites, y i Is the rainfall observed for station i, b is the window width,
an estimate of the amount of rainfall for stations other than station i given window width b.
Optionally, the geographical weighted regression model of the site is as follows:
wherein,
is a rainfall observation, β, of station i i0 Intercept terms for station i, X ik Is the kth auxiliary variable, beta, of site i ik Is the regression coefficient of the kth auxiliary variable of site i, p is the number of auxiliary variables of site, ε i Is the residual result.
Optionally, the regression coefficient matrix of the station i is obtained by solving according to the following formula:
wherein,
is a matrix of regression coefficients for site i,
regression coefficients including the intercept term of site i and p auxiliary variables, W i Is a diagonal matrix of n x n, W i Each non-zero element on the diagonal is a weight function of the station i and any other station in the window width range, X is an auxiliary variable matrix, X comprises each auxiliary variable of each station in the window width range, Y is a dependent variable matrix, and Y comprises a rainfall observation value of each station in the window width range.
In another aspect, the present invention further provides a downscaling rainfall prediction system, which, when executed by a computer, executes the downscaling rainfall prediction method as described above.
According to the specific embodiment provided by the invention, the invention discloses the following technical effects:
the invention provides a method and a system for predicting downscaling rainfall, wherein a geographical weighted regression model for representing the relation between each parameter and a rainfall observation value is established by taking a rainfall observation value of a station as a dependent variable and a parameter for representing the geographical position, the terrain and/or the vegetation coverage degree of the station as an independent variable based on a geographical weighted regression algorithm, the rainfall grades are further divided for each station, a weight function integrating the station grades and the station intervals of each station is considered in resolving of the regression coefficients and the residual results in the geographical weighted regression model of the station, interpolation is further performed in grids under high resolution according to the resolved regression coefficients and residual results of each station to obtain the regression coefficients and the residual results of each grid, and finally, rainfall prediction data under each grid is obtained according to the regression coefficients of each grid, the residual results of each grid and the geographical weighted regression model to realize prediction of the high resolution rainfall data of a target area; according to the method, the grade and the site distance of each site are considered in the resolving process of the regression coefficient and the residual error result in the site geographical weighting regression model, so that the rainfall data prediction accuracy of the site sparse area is guaranteed compared with that of the traditional algorithm.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required in the embodiments will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for predicting downscaling rainfall according to embodiment 1 of the present invention;
fig. 2 is a detailed flowchart of step S3 in the method provided in embodiment 1 of the present invention;
fig. 3 is a flowchart illustrating a step S7 of the method according to embodiment 1 of the present invention;
fig. 4 is a flowchart of a specific example of the method provided in embodiment 1 of the present invention;
FIG. 5 is a comparison chart of visual results of the method provided in example 1 of the present invention, taking Fujian province as an example;
FIG. 6 is a graph comparing data results of Fujian province in the method provided in example 1 of the present invention;
fig. 7 is a schematic structural diagram of a downscaling rainfall prediction system according to embodiment 2 of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention aims to provide a downscaling rainfall prediction method and system, which can accurately predict high-resolution rainfall data.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Example 1:
the present embodiment provides a method for predicting downscale rainfall, which, as shown in a flowchart in fig. 1, includes the following steps:
s1, site grading: according to the historical rainfall data of each station in the target area, carrying out grade division on each station, and determining the rainfall grade of each station; in this embodiment, a natural fracture method is adopted to grade each station according to historical rainfall data of each station in a target area, and the rainfall grade of each station is determined.
S2, determining the bandwidth of the geographic weighted regression algorithm: based on a cross validation method, determining the window width of a geographical weighted regression algorithm according to the rainfall observation value of each station in the target area; specifically, in this embodiment, the window width of the geo-weighted regression algorithm is determined according to the following formula:
wherein, b best The window width of the geographic weighted regression algorithm determined based on the cross validation method is defined, n is the number of sites, y i Is the rainfall observed for station i, b is the window width,
is an estimate of the amount of rainfall for stations other than station i given window width b.
S3, determining a weight function between sites: determining a weight function between any two stations based on the rainfall level and the window width of each station and the space distance between every two stations; as shown in fig. 2, step S3 specifically includes:
s31, determining the level weight between any two stations according to the rainfall level of each station; as in this embodiment, the rank weight between any two sites is determined according to the following equation:
wherein,
is a rank weight between site i and site j, C ij Is the rank difference between site i and site j, C max Is the maximum value of the grade difference.
S32, determining the distance weight between any two stations according to the space distance between every two stations and the window width; determining a distance weight between any two sites according to:
wherein,
as a distance weight between site i and site j, d ij Is the spatial distance between site i and site j, and b is the window width.
S33, determining a weight function between any two sites according to the grade weight between any two sites and the distance weight between any two sites; determining a weight function between any two sites according to:
wherein, W ij As a function of the weights between site i and site j,
as a rank weight between site i and site j,
the distance between site i and site j is weighted.
S4, establishing a geographical weighted regression model: aiming at any station, establishing a geographical weighted regression model of the station by taking the rainfall observed value of the station as a dependent variable and taking a plurality of auxiliary variables of the station as independent variables; the geographic weighted regression model comprises parameters to be determined; the parameters to be determined comprise regression coefficient matrixes of the auxiliary variables and residual error results. The secondary variables include parameters characterizing the geographic location of the site, the topography of the site, or the extent of vegetation coverage of the site, such as elevation, grade, longitude and latitude, and a normalized vegetation index for the site.
Specifically, in this embodiment, the geographical weighted regression model of the site is shown as the following formula:
wherein,
is a rainfall observation, β, of station i i0 Intercept terms for station i, X ik Is the k auxiliary variable, β, of site i ik Is the regression coefficient of the kth auxiliary variable of site i, p is the number of auxiliary variables of site, ε i Is the residual result.
S5, resolving the geographical weighted regression model: aiming at the geographical weighted regression model of any site, solving to obtain a regression coefficient matrix and a residual error result in the geographical weighted regression model of the site according to a weight function between the site and each site except the site in a window width range; the window width range is an area centered on the station and having the window width as a radius.
Solving to obtain a regression coefficient matrix of the station i according to the following formula:
wherein,
is a matrix of regression coefficients for site i,
regression coefficients comprising the intercept term of station i and p auxiliary variables, W i Is a diagonal matrix of n x n, W i Each non-zero element on the diagonal is a weight function of the station i and any other station in the window width range, X is an auxiliary variable matrix, X comprises each auxiliary variable of each station in the window width range, Y is a dependent variable matrix, and Y comprises a rainfall observation value of each station in the window width range.
S6, carrying out interpolation downscaling refinement on data in the target area: interpolating in a target area according to a regression coefficient matrix in the geographical weighted regression model of each site and a residual error result of each site to obtain the regression coefficient matrix and the residual error result of each grid under high resolution; in this embodiment, a common kriging method is used to perform interpolation in the target region to obtain a regression coefficient matrix and a residual error result of each grid under high resolution.
S7, grid rainfall prediction: predicting the rainfall of each grid according to the regression coefficient matrix and the residual error result of each grid under the high resolution to obtain the rainfall pre-estimated value of each grid; as shown in fig. 3, step S7 specifically includes:
s71, aiming at any grid under the high resolution of the target area, determining a rainfall non-residual estimation value of the grid according to a regression coefficient matrix and an auxiliary variable value of the grid.
And S72, obtaining the rainfall estimation value of the grid according to the rainfall non-residual estimation value of the grid and the residual result of the grid.
The following describes, with reference to a specific example, a method for predicting downscale rainfall, where the method for predicting downscale rainfall includes the following steps:
(1) Site ranking
According to weather station rainfall data, 5 grades of stations are divided based on the annual average rainfall value, and grade values of all the stations are obtained.
(2) Determining independent and dependent variables
The dependent variable in the regression algorithm is a station rainfall value, and the independent variable is reanalysis data of elevation, gradient, longitude and latitude, normalized vegetation index NDVI and IMERG rainfall of a corresponding station.
(3) Construction of site-level-based geographical weighted regression model
a. Determining window width
Determining an optimal window width based on a Cross Validation (CV) method; the cross validation algorithm comprises the following specific steps: the sites are divided into 10 sections (hereinafter referred to as 'folds'), i.e., each fold contains 10% of the total sites. In order to ensure that the sites of each fold are approximately uniformly distributed, firstly, a K-means clustering method is adopted to divide all the sites into N/10 categories, then one site is randomly selected from each category and is not placed back, the N/10 sites required by one fold can be obtained, the extracted fold is used as a verification set, the rest (N-N/10) sites are used as a training sample set, and the process is carried out for ten times, so that each fold of the sites can be used as the verification set for verification.
The formula for cross-validation CV is expressed as:
wherein, b best The window width of the geographic weighted regression algorithm determined based on the cross validation method is shown in the specification, wherein n is the number of sites, y i Is the rainfall observation value of the station i, b is the window width,
is an estimate of the amount of rainfall for stations other than station i given window width b.
b. Determining a distance weighting function
The algorithm adopts a Gaussian kernel function method to calculate the distance weight, adopts a continuous monotone attenuation function to represent the continuous monotone decreasing between the weight and the distance, and can overcome the defect of discontinuous space weight function. The distance function commonly used includes a distance threshold method, a distance inverse ratio method, and the like, in this embodiment, a gaussian function is used to determine the distance weight, and the function form is as follows:
where b is a defined bandwidth, d ij The distance of the jth peripheral site from the central site i within the bandwidth,
i.e. the correspondingly determined weights.
c. Determining a rank weighting function
Besides the inter-site distance factor, the rainfall level calculated by each site is also considered, and the rainfall level of each site is expressed as follows:
wherein
Representing each rank value, the corresponding site rank gap can be represented as follows:
the larger the grade difference between the sites is, the larger the difference between the two sites is, the smaller the corresponding grade weight is, and thus the grade weight function can be expressed as follows:
here, ,
and when the regression central point is i, the grade weighted values of the site i and the site j are represented. According to the result of the defined grade value, the grade difference between sites is 4 (5 minus 1) at most, and the grade weight range is between 0 and 1.
d. Calculating a total weight function
From the combination of the distance weight and the rank weight, the final weight function is obtained as:
the downscaling rainfall prediction method provided in this embodiment considers the distance element and also considers the influence caused by the property difference of the station itself, that is, the rainfall level difference of the station. Thus, W ij Finally, the total weight of the distance and the grade is integrated by the above formula. When the station level difference is 0 (C) ij = 0), the rank weight is 1, when the total weight degenerates to the distance weight in the general equation.
(4) Performing a site-level based geo-weighted regression process
All the sites within the calculation range (window width) are included in the calculation with any one of the sites as the center and the window width b as the radius. The closer the distance to the central station, the greater the weight; the smaller the grade difference with the central site is, the larger the weight is; and obtaining a regression equation of the central site, wherein the regression equation comprises a regression coefficient and a residual error result.
(5) Ending the site rank based geo-weighted regression process
And (5) repeating the step (4) until all the sites in the region are completely regressed, obtaining a regression coefficient matrix and a residual error result of the regression model of each site, and finishing the geographical weighted regression process based on the site level.
(6) Carrying out interpolation according to the regression coefficient and the residual error result of each station; in this embodiment, high resolution refers to a grid of areas of 1km × 1km resolution,
the residual results and the regression coefficients are interpolated into grids at the target region 1km × 1km resolution, respectively.
(7) Rainfall result estimation
And calculating the rainfall estimation value of the 1km × 1km resolution based on the interpolated 1km × 1km resolution regression coefficient.
(8) Fusion downscaling result calculation
And adding the residual error result of the 1km × 1km resolution rainfall estimation value to obtain final 1km × 1km resolution rainfall data.
Referring to fig. 4, step1 mainly illustrates the process of ranking the stations, which corresponds to (1): classifying the meteorological sites by classification operation representatives; NNA is a neighbor domain designation algorithm, and pixels of the raster image in the region under different resolutions are subjected to grade assignment according to the nearest meteorological station. Step2 illustrates the whole regression process and the process of interpolation after obtaining the residual error result and the regression coefficient; f represents 4 independent variables, namely elevation, gradient, longitude and latitude and normalized vegetation index, and the image resolution of the four variables is 1 x 1km; IMERG represents IMERG remote sensing re-analysis rainfall image, and the resolution is (0.1 degree, and is converted to km about 111.11 degree 111.1km); GUAGE is meteorological site data, and different colors and different grades; RGWR represents a site-level based geographically weighted regression process. The right-most graph shows that not only the distance weight but also the rank weight between different sites are considered in the regression process. The whole process represented by fig. 4 is mainly:
firstly, extracting F and IMERG values corresponding to each site as independent variables; then, taking the observed value of the meteorological site as a true value, and performing geographical weighted regression; the weight in the regression process adopts a weight value integrating the grade and the distance, and then a residual error value result (residual) and a regression coefficient result (Para _ F) corresponding to each meteorological site are obtained; interpolating the obtained residual error result to 1km × 1km, and performing neighbor domain assignment algorithm if the residual error result is interpolated to 1km × 1km and para _F, and assigning values according to points closest to the distance; note that the Para _ F obtained at this time is a series of independent variable parameter results, i.e., each independent variable (elevation, grade, longitude and latitude, etc.)A 1km × 1km image result is obtained after the NNA algorithm; EPRE H The result is obtained by multiplying and adding the regression coefficients by the corresponding F and IMERG, namely the estimation value which does not contain the regression residual error; MPRE H The final result is the addition of regression residues.
Fig. 5 shows the algorithm result of the present invention by taking fujian province as an example, the results of rainfall in 2001, 2008 and 2018 in each horizontal row from top to bottom are respectively: the IMERG rainfall reanalysis data results (0.1 degree), the 1km degree 1km results obtained by directly interpolating meteorological site data, the results obtained by calculating the regression method of the invention and the results of the geographical weighting regression algorithm which only uses distance weight and does not contain grade weight in the traditional algorithm. The third and fourth columns of results from the geoweighted regression contain more detail than the results from the direct interpolation of the second column because they contain characteristics of both site data and IMERG data, and further comparison of the third and fourth columns shows that the black boxes are more abundant and the details of the third column are closer to the results of the first and second columns. That is, using results that include rank weights may be better than results calculated using only distance weights.
Fig. 6 illustrates the superiority of the method provided in this embodiment from a data level, where the first row from top to bottom is an analysis of the 1km × 1km rainfall results and the actual site values obtained in this patent, the second row is an analysis of the results obtained only by distance weights and the actual site values, the third row is an analysis of the original IMERG rainfall re-analysis data and the actual site values, and the results in each image mainly have four values: RMSE (root mean square error), R2 (correlation coefficient), MAE (mean absolute error), BIAS (bayes BIAS), it can be seen that the results of the first row are all better than those of the second and third rows, that is, the 1km × 1km rainfall data product obtained by the method of the present invention is not only improved in spatial resolution compared to the original rainfall reanalysis data, but also better in data quality than the results obtained by the traditional geographical weighted regression algorithm using only distance weights.
In the embodiment, rainfall levels of all the sites are divided, the site levels and the site intervals of all the sites are considered in the calculation of the geographical weighted regression model of the sites, after the regression coefficients and the residual results of all the sites are obtained through calculation, interpolation is carried out in the grids under high resolution, the regression coefficients and the residual results of all the grids under high resolution are obtained, the regression coefficients and the residual results of all the grids are further brought into the geographical weighted regression model, rainfall data of all the grids are obtained, and prediction of high-resolution rainfall data of a target area is achieved.
Example 2:
the method of embodiment 1 of the present invention can also be implemented by means of the architecture of the downscaling rainfall prediction system shown in fig. 7. As shown in fig. 7, the downscaling rainfall prediction system may include a site level division module, a window width determination module, a weight function determination module, a regression model establishment module, and an interpolation downscaling module; some modules may also have sub-units for implementing their functions, for example including a distance weight determination unit and a level weight determination unit in the weight function determination module; the interpolation downscaling module comprises a regression coefficient matrix interpolation unit and a residual error result interpolation unit. Of course, the architecture shown in FIG. 7 is merely exemplary, and in some embodiments, other elements may be added to some of the modules; in addition, one or at least two components of the system shown in fig. 7 may be omitted as needed to implement different functions, depending on the actual needs.
Specific examples are used herein, but the foregoing description is only illustrative of the principles and embodiments of the present invention, and the description of the examples is only provided to assist understanding of the method and the core concept of the present invention; those skilled in the art will appreciate that the modules or steps of the invention described above can be implemented using general purpose computing apparatus, or alternatively, they can be implemented using program code executable by computing apparatus, such that it is executed by computing apparatus when stored in a storage device, or separately fabricated into integrated circuit modules, or multiple modules or steps thereof can be fabricated into a single integrated circuit module. The present invention is not limited to any specific combination of hardware and software.
Meanwhile, for a person skilled in the art, according to the idea of the present invention, the specific embodiments and the application range may be changed. In view of the above, the present disclosure should not be construed as limiting the invention.
Claims (10)
1. A method for predicting downscaling rainfall is characterized by comprising the following steps:
according to the historical rainfall data of each station in the target area, carrying out grade division on each station, and determining the rainfall grade of each station;
based on a cross validation method, determining the window width of a geographic weighted regression algorithm according to the rainfall observation value of each station in the target area;
determining a weight function between any two stations based on the rainfall level of each station, the window width and the space distance between every two stations;
aiming at any station, establishing a geographical weighted regression model of the station by taking the rainfall observed value of the station as a dependent variable and taking a plurality of auxiliary variables of the station as independent variables; the geographic weighting regression model comprises parameters to be determined; the parameters to be determined comprise a regression coefficient matrix of the auxiliary variable and a residual error result; the auxiliary variables comprise parameters for characterizing the geographical position of the site, the topography of the site or the vegetation coverage of the site;
aiming at the geographical weighted regression model of any station, solving to obtain a regression coefficient matrix and a residual error result in the geographical weighted regression model of the station according to the station and a weight function between the station and each station except the station in the window width range; the window width range is an area which takes the station as a center and the window width as a radius;
interpolating in a target area according to a regression coefficient matrix and a residual error result in the geographical weighted regression model of each site to obtain the regression coefficient matrix and the residual error result of each grid under high resolution;
and predicting the rainfall of each grid according to the regression coefficient matrix and the residual error result of each grid under the high resolution to obtain the rainfall pre-estimated value of each grid.
2. The method according to claim 1, wherein the predicting rainfall for each grid according to the regression coefficient matrix and the residual result of each grid under high resolution to obtain the rainfall estimate for each grid comprises:
aiming at any grid under the high resolution of a target area, determining a rainfall non-residual pre-estimated value of the grid according to a regression coefficient matrix of the grid and an auxiliary variable value of the grid;
and obtaining the rainfall prediction value of the grid according to the rainfall non-residual prediction value of the grid and the residual result of the grid.
3. The downscaling rainfall prediction method according to claim 1, wherein the determining a weight function between any two stations based on the rainfall level of each station, the window width, and the spatial distance between each two stations specifically comprises:
determining the grade weight between any two stations according to the rainfall level of each station;
determining the distance weight between any two stations according to the space distance between every two stations and the window width;
and determining a weight function between any two sites according to the grade weight between any two sites and the distance weight between any two sites.
4. The method of claim 3, wherein the distance weight between any two stations is determined according to the following equation:
wherein,
is the distance weight between site i and site j, d ij The space distance between the station i and the station j is defined, and b is the window width;
determining a rank weight between any two sites according to:
wherein,
as a rank weight between site i and site j, C ij As a grade difference between site i and site j, C max Is the maximum value of the grade difference;
determining a weight function between any two sites according to:
wherein, W ij As a function of the weights between site i and site j,
is a rank weight between site i and site j,
the distance between site i and site j is weighted.
5. The downscaling rainfall prediction method of claim 1, wherein the natural fracturing method is used to grade each site according to historical rainfall data of each site in the target area, and to determine a rainfall grade of each site.
6. The method of claim 1, wherein interpolation is performed in the target region by a common kriging method to obtain a regression coefficient matrix and a residual result of each grid at high resolution.
7. The method of claim 1, wherein the window width of the geoweighted regression algorithm is determined according to the following equation:
wherein, b best The window width of the geographic weighted regression algorithm determined based on the cross validation method is shown in the specification, wherein n is the number of sites, y i Is the rainfall observed for station i, b is the window width,
an estimate of the amount of rainfall for stations other than station i given window width b.
8. The method of claim 1, wherein the site's geo-weighted regression model is as follows:
wherein,
is the rainfall observed value, beta, of station i i0 Intercept term for station i, X ik Is the kth auxiliary variable, beta, of site i ik Is the regression coefficient of the kth auxiliary variable of site i, p is the number of auxiliary variables of site, ε i As a result of residual error。
9. The method of predicting downscaling rainfall according to claim 1, wherein the regression coefficient matrix of site i is obtained by solving according to the following equation:
wherein,
is a matrix of regression coefficients for site i,
regression coefficients comprising the intercept term of station i and p auxiliary variables, W i Is a diagonal matrix of n x n, W i Each non-zero element on the diagonal is a weight function of the station i and any other station in the window width range, X is an auxiliary variable matrix, X comprises each auxiliary variable of each station in the window width range, Y is a dependent variable matrix, and Y comprises a rainfall observation value of each station in the window width range.
10. A downscaling rainfall prediction system which, when executed by a computer, performs the downscaling rainfall prediction method of any one of claims 1 to 9.
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